Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension .a=W D 0:5/ and three-point bend .a=W D 0:1 and 0:5/ specimens under plane stress condition. The crack growth is controlled by the experimental J -integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack-tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress.

Size-dependent elasticity of nanocrystalline titania

Synchrotron-based high-pressure x-ray diffraction measurements indicate that compressibility, a fundamental materials property, can have a size-specific minimum value. The bulk modulus of nanocrystalline titania has a maximum at particle size of 15 nm. This can be explained by dislocation behavior because very high dislocation contents can be achieved when shear stress induced within nanoparticles counters the repulsion between dislocations. As particle size decreases, compression increasingly generates dislocation networks hardened by overlap of strain fields that shield intervening regions from external pressure. However, when particles become too small to sustain high dislocation concentrations, elastic stiffening declines. The compressibility has a minimum at intermediate sizes.

A field-consistent and variationally correct representation of transverse shear strains in the nine-noded plate element

We present a biquadratic Lagrangian plate bending element with consistent fields for the constrained transverse shear strain functions. A technique involving expansion of the strain interpolations in terms of Legendre polynomials is used to redistribute the kinematically derived shear strain fields so that the field-consistent forms (i.e. avoiding locking) are also variationally correct (i.e. do not violate the variational norms). Also, a rational method of isoparametric Jacobian transformation is incorporated so that the constrained covariant shear strain fields are always consistent in whatever general quadrilateral form the element may take. Finally the element is compared with another formulation which was recently published. The element is subjected to several robust bench mark tests and is found to pass all the tests efficiently.

Correlation of resistivity and microstructure in dilute titaniulll–nitrogen alloy

The precipitation kinetics of the quenched dilute Ti-1.6 at.-%N alloy has been followed by resistivity measurements at 77 K using the four probe method. Resistivity behaviour has been studied for various durations for the alloys aged in the temperature range 273-373 K. The resistivity behaviour has been explained on the basis of the growth and decay of interfacial strain fields associated with the precipitation process. In addition, the resistivity changes have been correlated with transmission electron microscopy observations. (C) 1995 The Institute of Materials.

Correlations between structure and thermodynamic properties of spinels and their applications in technology

Measurements a/the Gibbs' energy enthalpy and entrupy vffarmation oj chromites, vanadites and alumlnat.:s 0/ F", Ni. Co'. Mn, Zn Mg and Cd, using solid oxide galvanic cells over a ternperature range extending approximately lOOO°C, have shown that the '~'Ilir"!,,, J'JrIl/iJ~ tion 0/ cubic 2-3 oxide spinel phases (MX!O,), from component oxide (MO) with rock-salt and X.Os whir c(1f'l/!ldwn st!'llt'lw,·. call b,' represented by a semi-empirical correlalion, ~S~ = --LiS + L'i,SM +~S~:"d(±O.3) cal.deg-1 mol-1 where /',.SM Is the entropy 0/calian mixing oillhe tetrahedral alld octahedral sites o/the spinel and Sr:~ is tlie enfropy associaf,'d Wifh Ih,' randomization a/the lahn-Telier distortions. A review a/the methods/or evaluating the cation distriblltion lfl spille!s suggeJ{j' l/r,l! Ihe most promising scheme is based Oil octahedral site preference energies from the crystal field theory for the Iral1silioll IIIl'f"! IlIIL';. For I/""-Irallsifioll melal cal ions site preference energies are derived relative /0 thol'lt fLI, [ransilion metal ions from measured high tClllP('ftJi ure Cal iUlI disll iiJuriol1 in spine! phases thar contail! one IransilioJl metal and another non-transition metal carion. For 2-3 srinds compulatiorrs b,IS"J Oil i.!c[J;' Temkin mixing on each catioll subialtice predici JistributionJ that are In fair agreement with X-ray and 1I1'IIIrOll ditTraction, /IIdg""!ic dll.! electrical propcrries, and spectroscopic measurements. In 2-4 spineis mixing vI ions do not foliow strictly ideal slllIistli:al Jaws, Th,' OIl/up) associated with the randomizalion 0/the Jllhn-Teller dislOriioll" appear to be significant, only ill spinels witll 3d'. 3d', 3d' (ifld~UI' iOtls in tetrahedral and 3d' and 3d9 ions in octahedral positions. Application 0/this structural model for predicting the thermodynamic proputies ofspinel solid .,olutiofl5 or,' illustrated. F,lr complex systems additional contributions arising from strain fields, redox equilibria and off-center ions have to be qllalllififti. The entropy correlation for spinels provides a method for evaluating structure tran:.jormafiofl entropies in silllple o.\id.-s, ["founlllion on the relative stabilities ofoxides in different crystallCtructures is USe/III for computer ea/culaliof! a/phase dfugrullls ofIlIrer,',,1 III (N.lll1ie5 by method, similar to thost: used by Kaufman and Bernstein for refractory alloy systems. Examples oftechnoiogical appliCation tnclude the predictioll ofdeoxidation equilibria in Fe-Mn-AI-O s),slelll at 1600°C duj ,'Ulllpltfalion 0/phase relutions in Fe-Ni-Cr-S system,

Modeling of Piezocomposites using Variational Asymptotic Method

This work presents the development of piezocomposites made up of Macro Fiber Composites (MFCs) for aerospace applications and specifically involves, their computational analysis, material characterization and certain parametric studies. MFC was developed by NASA Langley Research Center in 1996 and currently is being distributed by Smart Material Co. 1] worldwide and finds applications both as an actuator as well as for sensor in various engineering applications. In this work, MFC is being modeled as an actuator and a theoretical formulation based on Variational Asymptotic Method (VAM) 2] is presented to analyse the laminates made up of MFCs. VAM minimizes the total electro-mechanical energy for the MFC laminate and approaches the exact solution asymptotically by making use of certain small parameters inherent to the problem through dimensional reduction. VAM provides closed form solutions for 1D constitutive law, recovery relations of warpings, 3D stress/strain fields and displacements and hence an ideal tool for carrying out parametric and design studies in such applications. VAM is geometrically exact and offers rigorous material characterization through cross-sectional analysis and dimensional reduction.

A Numerical Study of Indentation Using Indenters of Different Geometry

Finite element simulation of the Berkovich, Vickers, Knoop, and cone indenters was carried out for the indentation of elastic-plastic material. To fix the semiapex angle of the cone, several rules of equivalence were used and examined. Despite the asymmetry and differences in the stress and strain fields, it was established that for the Berkovich and Vickers indenters, the load-displacement relation can closely be simulated by a single cone indenter having a semiapex angle equal to 70.3degrees in accordance with the rule of the volume equivalence. On the other hand, none of the rules is applicable to the Knoop indenter owing to its great asymmetry. The finite element method developed here is also applicable to layered or gradient materials with slight modifications.

Analysis of a Rubber Cone Tensioned by a Concentrated Force

Using the constitutive equation of a rubber-like materials given by Gao (1997), this paper investigates the problem of a cone under tension of a concentrated force at its apex. Under consideration is the axial-symmetry case and the large strain is taken into account. The stress strain fields near the apex are obtained by both asymptotic analysis and finite element calculation. The two results are consistent well. When the cone angle is 180 degrees, the solution becomes that of non-linear Boussinesq's problem for tension case.

Singular behaviour near the tip of a sharp V-notch in a power law hardening material

This paper presents an asymptotic analysis of the near-tip stress and strain fields of a sharp V-notch in a power law hardening material. First, the asymptotic solutions of the HRR type are obtained for the plane stress problem under symmetric loading. It is found that the angular distribution function of the radial stress sigma(r) presents rapid variation with the polar angle if the notch angle beta is smaller than a critical notch angle; otherwise, there is no such phenomena. Secondly, the asymptotic solutions are developed for antisymmetric loading in the cases of plane strain and plane stress. The accurate calculation results and the detailed comparisons are given as well. All results show that the singular exponent s is changeable for various combinations of loading condition and plane problem.

Fracture analysis for 3-dimensional bodies with a surface crack

This paper deals with fracture analyses in 3-dimensional bodies containing a surface crack. A general solution of stress-strain fields at crack tip is proposed. Based on the stress-strain fields obtained, a high-order 3-dimensional special element is established to calculate the stress intensity factors in a plate with a surface crack. The variation of stress intensity factors with geometric parameters is investigated.

Local stresses and strains in axially cracked cylindrical shells

A perturbation solution is obtained for the local stress-strain fields in an axially cracked cylindrical shell. The tenth-order differential equations are used that take into account the transverse shear deformation. The perturbation of a curvature parameter, λ, is employed, where . The stress intensity factors for finite size cylindrical shells subjected to bending and internal pressure are evaluated. Sufficient accuracy can be obtained without using fine mesh sizes in regions near the crack tip. Also analyzed are the influence of cylinder diameter and shearing stiffness on bulging.

Study on cracked plates, shells and 3 dimensional bodies

This paper presents a summary of the authors' recent work in following areas: (1) The stress-strain fields at crack tip in Reissner's plate. (2) The calculations of the stress intensity factors in finite size plates. (3) The stress-strain fields at crack tip in Reissner's shell. (4) The calculations of the stress intensity factors and bulging coefficients in finite size spherical shells. (5) The stress-strain fields along crack tip in three dimensional body with surface crack. (6) The calculation of stress intensity factors in a plate with surface crack.

Study on cracked spherical shells

The local-global anatysis method is systematically extended to the fracture analysis of spherical shells. On the basis of the shallow shell theory, which takes into account transverse shear deformations, governing equations for cracked spherical shells expressed in displacement and stress functions f, F and φ are proposed, and then a general solution including Modes, Ⅰ, Ⅱ, Ⅲ for stress-strain fields at crack tip in a spherical shell is obtained, which plays the same role as Williams's expansion in plane elasticity. The numerical results for finite-size spherical shells under different boundary conditions have been obtained. Furthermore, the bulging factors are analyzed with regard to shearing stiffness and an approximate formula is given.

Evolution of Localized Damage Zone in Heterogeneous Media

Evolution of localized damage zone is a key to catastrophic rupture in heterogeneous materials. In the present article, the evolutions of strain fields of rock specimens are investigated experimentally. The observed evolution of fluctuations and autocorrelations of strain fields under uniaxial compression demonstrates that the localization of deformation always appears ahead of catastrophic rupture. In particular, the localization evolves pronouncedly with increasing deformation in the rock experiments. By means of the definition of the zone with high strain rate and likely damage localization, it is found that the size of the localized zone decreases from the sample size at peak load to an eventual value. Actually, the deformation field beyond peak load is bound to suffer bifurcation, namely an elastic unloading part and a continuing but localized damage part will co-exist in series in a specimen. To describe this continuous bifurcation and localization process observed in experiments, a model on continuum mechanics is developed. The model can explain why the decreasing width of localized zone can lead stable deformation to unstable, but it still has not provided the complete equations governing the evolution of the localized zone.

喜马拉雅西构造结区岩石圈演化三维有限元动力学数值模拟

The past three decades have seen numerous attempts to numerically model stress and strain patterns in the lithosphere of the Earth on both global and regional scales. This efforts have been indispensable in identifying the features we need to include in our endeavour to develop better models of our planet’s lithosphere and they have also raised our awareness for the many unresolved issue in the deep geodynamical issues that need to be addressed in the future. Nonetheless, in most models, the lithosphere is treated as a single layer with depth-averaged properties, and as the same distribution in the stress and strain fields, and as deforming under plane strain. All these above make a great hander for its reality and degree of recognition. As the beginning in this paper, some principal numerical models and results on the evolution of Tibetan plateau are reviewed and analyzed. Then, the geological and geophysical expedition on the Western Himalayan Syntaxis is briefly reviewed. Furthermore, we analysis the feature in deep geophysical field studies in this area and adjacent regions. Because, for most continents, stress models driven by plate boundary forces have successfully reproduced the main characteristics of the stress and strain field, we present a set of three-dimensional models of lithosphere system for a simplified geometry of the Western Himalayan Syntaxis area and its adjacent regions, where we try to match the first-order characteristics of the stress and strain fields of lithosphere since 10 Ma, and deformation and geodynamical evolution process in former 2Ma. Of course, the kinematic boundary conditions of the stress models driven by plate boundary forces were applied. The rheology plays a significant role in the lithospheric tectonics, which lead to different rheological parameters were used in different works although the have the same constitutive equations in models. So, in this paper we do not aim to produce all characteristics of the Western Himalayan Syntaxis areas’ stress and strain fields by the choices of various parameters, but rather the dynamic response between various rheological parameters and stress and strain fields. We have chosen to concentrate on the importance of rheology and lateral strength variations for lithospheric stress and strain patterns and use our findings to build a model of the Western Himalayan Syntaxis areas. In doing so, we want to go beyond purely elastic models or purely viscoelastic models. Compared the results of the crust viscosity in the Western Himalayan Syntaxis areas, we believed that, when various viscoelastic models are adopted, the selection of the coefficient of viscosity in the Western Syntaxis area has important influence on the its uplifts and evolutions. A wider uplift ranges and gently elevation was observed at the same time when a lower viscosity was used in our models, and vice versa. Data of stress magnitudes are not available, but it is clear that the stress levels must be at or below the failure threshold of rock under compression. Under these criteria, the calculation results show that the viscosity in the Western Syntaxis area should be smaller than 1023Pa.s When elastic model is adopted in relatively rigid Tarim basin, obvious changes are induced to the stress and strain fields of the whole Western Syntaxis area. We found that rigid block of lithosphere reduced stress levels within its interior and that, at the edges of such regions, stress orientation can change. Furthermore there is no evidence that such rigid regions act as stress barriers in that they shield areas in opposite sides of the structure from the influence of one another. In our models, the upper crustal material of the Western Syntaxis area does not turns to move westward. Whereas, because of the stress and strain fields have been decoupling at the interior of the lithosphere, we can get the results that the deep material must not move westward.